Question: A circle has a sector with area $5\pi$ and central angle $\dfrac{1}{10}\pi$ radian. What is the area of the circle? ${100\pi}$ $\color{#9D38BD}{\dfrac{1}{10}\pi}$ ${5\pi}$
The ratio between the sector's central angle $\theta$ and $2 \pi$ radians is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{2 \pi} = \dfrac{A_s}{A_c}$ $\dfrac{1}{10}\pi \div 2 \pi = 5\pi \div A_c$ $\dfrac{1}{20} = 5\pi \div A_c$ $A_c \times \dfrac{1}{20} = 5\pi$ $A_c = 5\pi \times 20$ $A_c = 100\pi$